PHYSICAL REVIEW B 84, 195443 (2011)

Electronic structure of graphene on single-crystal copper substrates

Andrew L. Walter,1,2,* Shu Nie,3 Aaron Bostwick,1 Keun Su Kim,1,4 Luca Moreschini,1 Young Jun Chang,1,2

Davide Innocenti,5 Karsten Horn,2 Kevin F. McCarty,3 and Eli Rotenberg1

1Advanced Light Source (ALS), E. O. Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA2Department of Molecular Physics, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany

3Sandia National Laboratories, Livermore, California 94550, USA4Center for Atomic Wires and Layers, Pohang University of Science and Technology, Pohang 790-784, Korea

5University of Rome (Tor Vergata), I-00173 Rome, Italy(Received 6 August 2011; published 9 November 2011)

The electronic structure of graphene on Cu(111) and Cu(100) single crystals is investigated using low-energyelectron microscopy, low-energy electron diffraction, and angle-resolved photoemission spectroscopy. On bothsubstrates the graphene is rotationally disordered and interactions between the graphene and substrate lead toa shift in the Dirac crossing of ∼−0.3 eV and the opening of a ∼250 meV gap. Exposure of the samplesto air resulted in intercalation of oxygen under the graphene on Cu(100), which formed a (

√2 × 2

√2)R45o

superstructure. The effect of this intercalation on the graphene π bands is to increase the offset of the Diraccrossing (∼−0.6 eV) and enlarge the gap (∼350 meV). No such effect is observed for the graphene on the Cu(111)sample, with the surface state at � not showing the gap associated with a surface superstructure. The graphenefilm is found to protect the surface state from air exposure, with no change in the effective mass observed, as forone monolayer of Ag on Cu(111).

DOI: 10.1103/PhysRevB.84.195443 PACS number(s): 73.40.−c, 73.20.At, 79.60.Dp

I. INTRODUCTION

Graphene’s unique electronic properties1 have excitedintense research interest since its isolation by micromechanicalcleavage in 2004.2 However, this technique, used in theseearly investigations, is unsuitable for large-scale productionof graphene sheets. Thermal decompositon of SiC,3–6 surfacesegregation of C dissolved in metal substrates,7–9 and decom-position of hydrocarbons at metal surfaces10,11 have all beenshown to produce graphene and are potentially scalable tocommercial production.

Recently the growth of large-scale graphene films(∼1 m wide) has been accomplished using chemical vapordeposition (CVD) onto polycrystalline Cu foils,12 leading toa strong interest in the electronic and structural propertiesof the graphene/Cu interface. The structural properties ofgraphene/Cu was investigated13 in detail; however, electronicstructure data, particularly angle-resolved photoemission spec-troscopy (ARPES), on such films are hampered by the manyrandomly oriented domains in both the graphene and thesubstrate. This leads to a large collection of electronic bandsfrom both the substrate and the graphene, greatly confusingthe interpretation of the ARPES data.

Recently, Varykhalov et al. attempted to overcome thisproblem by measuring graphene on one monolayer ofCu/Ni(111), which indicated that the interaction betweengraphene and the substrate was significantly underestimatedby the current DFT L(S)DA theory.14 The method involvedgrowing a graphene film on a 15- to 20-monolayer Ni(111) filmon W(110) followed by intercalating a monolayer of Cu(111)underneath the graphene. While providing insight into theelectronic structure of graphene on Cu, it is an open questionwhether this arrangement reflects the properties of the interfacebetween graphene and bulk copper. The growth of grapheneon single-crystal Cu, undertaken in the current study, providesan ideal system for investigating the electronic structure of

graphene on Cu by eliminating the rotational disorder in thesubstrate. As the bulk and surface Cu bands are well known,in our samples it is easy to identify the graphene π bands.

Graphene films were grown on Cu(111) and Cu(100)single crystals and characterized using low-energy electronmicroscopy (LEEM) and low-energy electron diffraction(LEED). The electronic structure of the graphene samples wasinvestigated using ARPES measurements. Here we show that,similarly to graphene on one monolayer (ML) of Cu/Ni(111),14

graphene on Cu (100) and (111) single crystals is n-doped withthe Dirac crossing energy ED located −0.3 eV below the Fermilevel EF . We find a gap of ∼250 meV at the Dirac crossingof the graphene π bands, significantly larger than the gap ingraphene on 1 ML of Cu/Ni(111) (∼180 meV) and the LDAestimate (∼11 meV).15

We also show that air exposure leads to oxygen intercalationunder the graphene on Cu(100), forming a (

√2 × 2

√2)R45o

superstructureand giving a larger doping (∼−0.6 eV Diraccrossing shift) and an increased gap (∼350 meV in thegraphene π bands at ED). The Cu(111) surface state at �

(Brillouin zone center) does not show the gap expected for suchan intercalated surface structure, confirming that exposure toair does not produce the same effect for graphene on Cu(111).In contrast, the graphene protects the surface state at � fromair exposure, with no change in the effective mass observed.

II. METHODS

Cu(100) and Cu(111) single crystals were initially cleanedby annealing at 900 ◦C for about 12 h in a flowing mixtureof hydrogen and argon at atmospheric pressure followed bysputtering with argon ions. Subsequent annealing at 750 ◦Cin the LEEM produced surfaces with atomically flat terracesseparated by monatomic Cu steps and step bunches. Largebunches of steps formed on Cu(111) at pinning sites spaced

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ANDREW L. WALTER et al. PHYSICAL REVIEW B 84, 195443 (2011)

about 2–5 μ apart. Carbon was deposited onto the substratesat 850–900 ◦C from a graphite rod heated by an electronbeam. The growth was imaged in real time using LEEM.The deposition was stopped near the completion of the firstgraphene layer using the ability of LEEM to distinguish bareCu, monolayer graphene, and bilayer graphene.16,17

Selected-area LEED patterns were acquired after growthfrom regions 2 or 20 μm in diameter. The graphene-covered Cucrystals were removed from the ultrahigh vacuum of the LEEMsystem and exposed to air for about 3 h before again beingplaced in vacuum and degassed at about 350 ◦C for ARPESmeasurements. After the ARPES measurements, the sampleswere reintroduced into the LEEM for further analysis. Boththe graphene/Cu(100) and graphene on Cu(111) specimensexperienced an additional 3 h of exposure to air while thegraphene/Cu(111) was also kept in a desiccator for severalweeks prior to analysis. The samples were briefly degassed atabout 250 ◦C before the subsequent LEEM/LEED measure-ments. The LEEM/LEED measurements were performed atSandia National Laboratories in Livermore, California.

ARPES spectra were obtained at the Electronic StructureFactory end station (SES-R4000 analyzer) at beamline 7 ofthe Advanced Light Source, Lawrence Berkeley NationalLaboratory. A photon energy of 95 eV was used, givingoverall resolutions of ∼25 meV and ∼0.01 A−1. The spatialarea sampled by the ARPES spectra was typically 50 to100 μm. During the measurements the samples were cooledto ∼20 K using a liquid He-cooled cryostat and the pressurewas <2 × 10−10 Torr.

The ARPES spectrum of graphene on Cu single crystalswas modelled as follows. The bare π -band dispersion Ebare(k)was computed using a first nearest-neighbor tight binding (TB)model based on the approach given by Saito et al.18 The secularequation |H − Ebare±(k)S| = 0 is solved for the eigenvaluesEbare±(k), with

H =[

ε2p − Egap/2 γ0f (k)γ0f (k)∗ ε2p − Egap/2

],

(1)

S =[

1 s0f (k)s0f (k)∗ 1

],

and

f (k) = exp(ikR1 + ikR2 + ikR3), (2)

where γ0 is the hopping potential, s0 is the overlap potential,and R1,R2,R3 are the vectors denoting the position of the threefirst nearest-neighbor carbon atoms.

A lattice constant, a = 2.46, is employed as are the fittedparameters, γ0 = −3.24 eV and s0 = 0.0425 eV, determinedby Bostwick et al. for graphene on (6

√3 × 6

√3)R30 ◦ C-

SiC(0001).19 The fitted parameter, ε2p, is the offset of theDirac energy, ED , from the Fermi level due to doping of thegraphene by the substrate and is determined by comparisonto the graphene on Cu ARPES measurements. The Egap

parameter is introduced by us to account for the introductionof an energy gap at ED due to the breaking of graphene’s A-Blattice symmetry. Broadening of the bare band is introduced

FIG. 1. (Color online) Experimental fermi surface and π bandstructure obtained from graphene on (6

√3 × 6

√3)R30 ◦ C-SiC (a i,

ii, and iii) for comparison to a semiempirical model (b i, ii, and iii).The model employs a first nearest-neighbor tight binding model forthe bare (unbroadened) bands with the parameters (γ0 = −3.24 eV,s0 = 0.0425 eV, and ε2p = −0.47 eV) determined from a fit to theexperimental data. Broadening is performed using the self-energy,obtained by a fit to the experimental data in the �-K direction, andexperimental broadening of 25 meV and 0.01 A−1. The simulationand experiment agree qualitatively.

to the model through the self-energy via the single-particlespectral function as follows:

A(E,k) = |Im�(E,k)|(E − Ebare(k) − Re�(E,k)2) + Im�(E,k)2 .

(3)

The self-energy, �(E,k), is determined using the semiem-pirical method of Bostwick et al.,20 where the linewidth of theARPES data is used to determine the imaginary componentof the self-energy, which is Hilbert transformed to get thereal component. This experimental self-energy is then usedto recreate the experimental data and a self-consistent fittingused to further refine the self-energy. An additional Gaussianbroadening term is added to the current model to accountfor experimental broadening in energy, �E = 25 meV, andmomentum, �k = 10 mA−1. Figure 1 shows experimentaldata for graphene on (6

√3 × 6

√3)R30 ◦ C-SiC(0001) (data

adapted from Bostwick et al.20) compared to a model spectralfunction fitted according to the above procedure. The fittedvalues, excepting ε2p and Egap, used for the graphene on theCu data model are those obtained from this fit as the rotationaldisorder prohibits fitting in this case.

For comparison to the graphene on single-crystal Cuexperimental data many rotationally disordered domains needto be modeled. This is done by producing a 3D (2 momentumand 1 energy) spectral function for a single graphene domain,as shown in Fig. 1. This single domain is then rotated aroundthe � point (in this case 20 single domains, with evenlyspaced rotation angles between ±2.5 ◦) to produce the spectralfunction from 20 rotationally disordered graphene domains.The rotational disorder model is then produced by summingthe spectral function from each of these rotational domainstogether. Inclusion of additional domains, or domains withlarger rotations, did not appreciably change the resultingspectral function, hence, these values were employed.

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FIG. 2. (Color online) LEEM/LEED characterization of a nearlycomplete single-layer graphene film on Cu(111). (a) LEEM imagewith a 20-μm field of view. Bright dots are nucleation sites and brightlines are boundaries between graphene islands. (b) LEED from a20-μm-diameter area of (a). First-order diffraction spot of Cu markedby red arrow and portion of graphene arc marked by blue arrow.

III. RESULTS AND DISCUSSION

A. LEEM of as-grown films

Figures 2(a) and 3(a) show representative LEEM micro-graphs of graphene on Cu(111) and Cu(100), respectively.These images show that graphene grows in grains separatedby boundaries, whose intensity can be bright or dark de-pending on the electron energy used for imaging. The brightdots in Fig. 2(a) are the graphene nucleation sites. Similargrowth structures have been observed in scanning tunnelingmicroscopy (STM) measurements of graphene on Cu(100).21

Figures 2(b) and 3(b) show representative LEED patternsintegrated over the 20-μm regions of Figs. 2(a) and 3(a)for Cu(111) and (100), respectively. The LEED patternobtained from graphene on Cu(111) consists not of six sharpspots expected for a perfect graphene sheet but, instead, issmeared into a nearly compete ring. This shows that graphenegrows on Cu(111) with a substantial amount of azimuthaldisorder. The graphene diffraction is most intense near thefirst-order Cu(111) spots, indicating a preference for grapheneto align with the Cu lattice. Subsequent growth experimentsestablished that the graphene not aligned with the Cu(111)substrate originated from islands that nucleated at the largebunches of Cu steps.22 Reducing the bunch density leads tohigher fractions of aligned graphene. The graphene LEED

pattern is also markedly broadened in the radial direction, aresult of the Cu hillocks that form when uncovered Cu sublimesduring graphene growth.13 The broadening of the grapheneLEED pattern in the radial direction results from the fact thatthe graphene conforms to this roughened topography.

The LEED pattern obtained from graphene on the Cu(100)crystal is similar to that from Cu(111) crystals and (100) grainsof copper foils. The LEED pattern consists of broad arcs.While the average pattern has two sets of sixfold arcs,13 oneset is stronger in Fig. 3(b). The two sets of arcs arise becausethere are two symmetry-equivalent ways to put the sixfoldgraphene on the four-fold Cu(100) surface. The arcs occurbecause the graphene has a large range of in-plane orientations.In addition, the arcs are broadened in the radial direction, aresult of the roughened surface topology, as for Cu(111) andSTM measurements.21 Reducing the integration area for theLEED patterns down to 2 μ does not completely eliminatethe azimuthal disorder observed in the LEED patterns for bothCu(100) and Cu(111). Therefore, the size of a domain havinga single in-plane orientation is smaller than the typical grainsseen in Figs. 2(a) and 3(a).

B. Angle resolved photoemission spectroscopy

Angle-resolved photoemission spectroscopy (ARPES)measurements of graphene on Cu(111) and Cu(100) surfacesare presented in Figs. 4 and 5, respectively. The Fermi surfaceof the graphene on Cu(111) is presented in Fig. 4(a). Thelarge nearly continuous arc (indicated by the large dashed line)corresponds to the Fermi surface of the rotationally disorderedgraphene π bands. Similar to the LEED pattern presentedabove, an increase in the intensity in the Cu(111) �-K directionis observed. This is the direction along which the two latticesare aligned. The other features in Fig. 4(a) correspond to cutsthrough the Cu(111) Fermi surface and the central circulararc of the Cu(111) surface state.23,24 Since the clean Cu(111)surface state does not survive exposure to air and since theLEEM images show that the substrate is covered, the surfacestate observed here must be localized to the interface betweengraphene and Cu(111).

The experimental spectral function obtained along the whiteline in Fig. 4(a) is presented in Fig. 4(b) with the TB fit obtainedusing ε2p = −0.3 eV (dashed blue line). The good agreement

FIG. 3. (Color online) LEEM/LEED characterization of single-layer graphene film on Cu(100). (a) LEEM image with a 20-μm field ofview. Dark lines are boundaries between graphene islands. (b) LEED from 20-μm-diameter area of as-grown graphene. One graphene arcmarked by a blue arrow. (c) LEED from a 2-μm-diameter area of air-exposed sample. Diffraction spots of Cu, graphene, and intercalated Oare denoted by red, blue, and green arrows, respectively.

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πε

FIG. 4. (Color online) Experimental Fermi surface (a) obtainedfrom graphene on single-crystal Cu(111). Also presented is theexperimental spectral function (b), semiemperical model spectralfunction (c), energy distribution curves (d), and momentum distri-bution curves (e) obtained along the white line in (a) (Cu Brillouinzone �-K direction). The graphene π bands calculated from afirst nearest-neighbor tight binding model (γ0 = −3.24 eV, s0 =0.0425 eV, and ε2p = −0.3 eV) are overlayed as the large dashedblue lines. A parabolic fit to the Cu(111) surface states is also shown(small dashed yellow lines). All other unmarked bands are due to thebulk Cu. The graphene Fermi surface is observed as an uninterruptedring due to rotationally disordered graphene domains. The preferentialalignment (higher intensity) of the domains along the �-K directionis also observed in LEED.

between the TB fit and the experimental data indicates that thegraphene is electron (n-type) doped by the Cu layer. The effectof this doping is a shift in the Dirac crossing to −0.3 eV, ingood agreement with data obtained from graphene on 1 ML ofCu/Ni(111)14 (−0.31 eV).

Varykhalov et al.14 also found that a gap was opened atthe Dirac point (∼180 meV) in the graphene on 1 ML ofCu/Ni(111) system. At first glance the spectral function inFig. 4(b) also suggests a gap for graphene on single-crystal Cu;however, the energy distribution curves (EDC) and momentumdistribution curves (MDC) shown in Figs. 4(d) and 4(e)indicate intensity is present throughout the Dirac crossingregion which suggests the presence of states. Analysis showsthat this intensity is largely caused by the smearing of thebands due to rotational disorder, which provides an additionallevel of complexity. An accurate assessment of the size ofthe gap requires taking the rotational disorder into account, asdiscussed next.

The predicted EDC obtained from the rotational disordermodel described above, labeled G111, with different simulatedgaps are shown (solid blue lines) in Fig. 6(a). The mostsignificant change with gap size is reducing the depth of theminima at the Dirac crossing (∼−0.3 eV). The experimentalEDC curve is overlayed (dashed red line) on three EDCcurves (Eg = 270, 250, and 230 meV). The best fit betweenexperiment [Fig. 4(b)] and theory [Fig. 4(c)] is obtainedwhen a gap of ∼250 meV is used in the model. This is anappreciably larger gap than was found for graphene on 1 MLof Cu/Ni(111),14 Eg = 180 meV, which indicates a strongerinteraction between the graphene and single-crystal Cu. Wefind that the doping level and band gap does not vary aroundthe π band arc.

FIG. 5. (Color online) Experimental Fermi surface (a) obtainedfrom graphene on single-crystal Cu(100). Also presented is the exper-imental spectral function (b), semiemperical model spectral function(c), energy distribution curves (d), and momentum distribution curves(e) obtained along the white line in (a) (Cu Brillouin zone �-Kdirection). The graphene π bands calculated from a first nearest-neighbor tight binding model (γ0 = −3.24 eV, s0 = 0.0425 eV, andε2p = −0.3 eV) are overlayed as the dash-dot blue and dash-dot dotgreen lines, respectively. All other unmarked bands are due to thebulk Cu. The graphene Fermi surface is observed as an uninteruptedring due to rotationally disordered graphene domains.

In contrast to the above analysis, a mere visual inspection ofthe data in Figs. 4(b) and 5(a) would suggest a much larger gap,around 350 to 400 meV. This demonstrates that the rotationalsmearing of the spectral function due to azimuthal disorder isto artificially enhance the gap size by up to 60%.

The graphene on Cu(100) Fermi surface is shown inFig. 5(a), where the graphene ring is twice as broad as forgraphene on Cu(111), Fig. 4(a). The nearly continuous arc ofthe π band is consistent with the large amount of rotationaldisorder observed in LEED [Fig. 3(b)]. Moreover, the graphenering on Cu(100) is twice as broad as that on Cu(111). Thespectral function along the white line in Fig. 5(a), shownin Fig. 5(b), indicates a shoulder (green dash-dot-dot line)offset from the main band ( dash-dot blue line). The TBfit (dash-dot-dot green line) describes this shoulder well inFigs. 5(a) and 6(b). Although the main peak in Fig. 5 canbe described by the same TB fit, a higher Dirac crossingoffset (ε2p = −0.6 eV) is obtained by the fitting. The extrawidth of the Fermi surface can, therefore, be ascribed to twodistinct doping levels for graphene on single-crystal Cu(100).The origin of the two doping levels will be discussed in thenext section; however, it is important to note that one doping

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ELECTRONIC STRUCTURE OF GRAPHENE ON SINGLE- . . . PHYSICAL REVIEW B 84, 195443 (2011)

π πε ε

FIG. 6. (Color online) The energy distribution curves (dashedred lines) obtained at the K point from the semiempirical modelfor a range of simulated band gaps (solid blue lines) are presentedfor (a) Cu(111), together with a single-band model G111 whose gapEg(G111) is varied, and [(b) and (c)] for Cu(100), which is comparedto a two-band model GA

100, GB100. In (b), the gap Eg(GB

100) is varied forfixed Eg(GA

100) = 250 meV, while in (c), the gap Eg(GA100) is varied for

fixed Eg(GB100) = 350 meV. In all panels, the light blue lines represent

best-fit models to the data.

level is the same as the graphene in single-crystal the Cu(111)case (G111 in Fig. 4 and GA

100 in Fig. 5) and an extra dopinglevel most likely due to some difference in the sample (GB

100in Fig. 5).

Similar to graphene on single-crystal Cu(111), Figs. 4(d)and 4(e), the EDC and MDC plots in Figs. 5(d) and 6(e)indicate intensity in the region of the Dirac crossings. Todetermine the size of the gap in both doping levels (GA

100and GB

100) it is once again necessary to compare the EDCcurves at the K point from the rotational disorder model andthe experimental data. In this case, the model is extended bycreating the 3D spectral functions, as used in the graphene onCu(111), for each of the two doping levels indicated by the TBbare bands in Fig. 5 and summing them together. The EDCcurves at the K point (solid blue lines) are shown for differentsimulated gaps in the GB

100 [Fig. 6(b)] and GA100 [Fig. 6(c)]

bands, respectively. In Fig. 6(b) the GA100 band gap is set to

250 meV and in Fig. 6(c) the GB100 band gap is set to 350 meV.

The overlying experimental EDC (dashed red lines) give thebest fit for a gap in the GB

100 band [Fig. 6(b)] of 350 meV anda gap in the GA

100 band [Fig. 6(c)] of 250 meV.The model spectral function obtained based on the two TB

bare bands from Fig. 5 and the band gaps Eg(GA100) = 250 meV

and Eg(GB100) = 350 meV is shown in Fig. 5(c), and it matches

well with the experimental spectral function in Fig. 5(b). Astructural origin for the two doping levels, where two facets onthe surface produce a momentum offset of two similarly dopedgraphene domains, was also considered. The model spectralfunction for such a system did not reproduce the shape of theexperimental EDC plots in Figs. 6(b) and 5(c) and, therefore,is discounted. Such facetted features were also not observedin STM measurements of Rasool et al.21

Summarizing the ARPES data, graphene bands Cu(111)and Cu(100) (G111 and GA

100, respectively) were observedwith identical gaps (Eg = 250 meV) and doping levels (ε2p =−0.3 eV). A second graphene band (GB

100) was observed onCu(100), with a larger gap (∼350 meV) and doping level(∼0.6 eV). This implies that the interaction of the graphene

with the substrate layer is substantially stronger in the GB100

doping regions.The interactions between graphene and metal substrates

has been modeled extensively using DFT L(S)DA theory25

and by considering van der Waals interactions using variationson vdW-DF theory.26 Khomyakov et al.,25 in addition tocalculating the band structure, investigated the effect ofvarying the bond distance between the graphene layer anda metallic substrate. For graphene on Cu(111) they found thatvarying the bond distance from 3 A to 4 A can shift the Diraccrossing from ∼−0.5 eV to ∼+0.25 eV. The close agreementof the Dirac crossing for graphene on single-crystal Cu(111),graphene on single-crystal Cu(100), and graphene on 1 ML ofCu/Ni(111)14 therefore indicates that the graphene-Cu bonddistance is similar in all cases.

On both Cu(111) and (100) the spectral function does notvary appreciably around the arc of the graphene π band.That is, doping level and band gap do not change withthe in-plane orientation of the graphenes. Furthermore, theDirac crossing values (dopings) and band gaps are similaron the two Cu surfaces. Therefore, the electronic structure ofgraphenes is not very sensitive to the physical and electronicstructures of the Cu surfaces or the precise alignment of thefilm/substrate lattices. These observations suggest relativelyweak interactions between the film and the Cu. But there aresufficient interactions to dope the graphene and open a bandgap by breaking the symmetry of the graphene lattice. Thelarger band gap on the Cu single crystals compared to grapheneon 1 ML of Cu/Ni(111)14 may result from greater substrate-induced symmetry breaking. This is in contrast to the DFTcalculations, which predict only a small band gap (11 meV).15

C. Air-exposed films

To gain insight into the origin of the two doping levels ob-served for graphene on Cu(100), the sample was re-examinedby use of LEEM/LEED after the ARPES experiments. Afterdegassing at about 250 oC, the LEEM images were indistin-guishable from the as-grown film. However, Fig. 3(c) revealsnew LEED features: four weak, radial lines rotated 45o relativeto the directions of the first-order Cu spots.27 At the ends ofthe lines are weak spots (see green arrow) separated by

√2

times the length of the Cu reciprocal lattice. This pattern canbe interpreted as induced by the interaction of air with thegraphene/Cu(100) system. Since graphene on other substratessurvives air exposure and is cleaned easily with annealing at300 ◦C, it is likely that the effect represents intercalation of anatmospheric species between the graphene and the copper.

As shown by LEED and STM,28,29 annealing oxygenadsorbed on Cu(100) at about 300 oC forms two domains with(√

2 × 2√

2)R45o symmetry at a saturation coverage of onehalf of a monolayer. Since our samples were annealed to asimilar temperature after transferring them through the air tothe ARPES chamber, it is likely that we are observing theintercalation of oxygen between the graphene and the Cu(100)surface. In our case, the intercalated oxygen is not well ordered,giving lines rather than strong LEED spots.

Auger electron spectroscopy (AES), not shown here,confirmed that the air-exposed sample contained oxygen.Surveying the surface by examining LEED from areas 2 μm in

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FIG. 7. (Color online) Detailed experimental band structure of theCu(111) surface state. The dashed yellow line denotes the parabolicfit used to determine the values in Table I.

diameter established that the intercalation was uniform on thislength scale. However, we cannot exclude spatial variationsin oxygen content at smaller length scales. Thus, we proposethat the two doping levels of graphene on Cu(100) observedin ARPES arise from intercalated and nonintercalated regions,which would lead to two different levels of charge transferto the graphene. The effect of the oxygen on the graphenethen also acts to increase the size of the gap from ∼250 to∼350 meV. It is interesting that in their study of graphene on1 ML of X/Ni(111), with X being Cu, Ag, or Au, Varykhalovet al.14 also found that the band gap became larger withincreasing doping. We see a similar increase in the band gapfor the oxygen intercalated region, which has a higher dopinglevel.

Even lengthy air exposure did not change the LEEM imagesand LEED from the graphene/Cu(111) specimen. However,AES revealed the presence of oxygen. Previous studies haveestablished that adsorbed oxygen on Cu(111) does not formordered structures and changes the work function less than15 meV.30 While we cannot totally exclude some oxygenintercalation on air exposure for graphene/Cu(111), the neteffect is a uniform doping of the graphene.

D. Cu(111) surface state

An important feature of the graphene on the Cu(111) Fermisurface [Fig. 4(a)] is the well-known Cu surface state at �

indicated by the small circle (dashed yellow line). Previousmeasurements31 have shown that one monolayer of Ag onCu(111) reduces the bandwidth of this state by a factor of0.55 and renormalizes the effective mass by a factor of 0.88.The spectral function of the surface state is shown in Fig. 7,

TABLE I. Cu(111) surface state data. The effective mass isunchanged by the graphene overlayer, in contrast to 1 ML of Agon Cu(111).31

Substrate Bandwidth Fermi Effective(eV) vector mass

(A−1) (m*/me)

Cu(111)31 0.435 0.215 0.411 ML Ag on Cu(111)31 0.241 0.151 0.361 ML G on Cu(111) 0.218 0.150 0.39

with a parabolic fit to the state shown in yellow (small dashedlines) in Fig. 4(a) and Fig. 7. Parameters from the parabolicfit are used to determine the bandwidth and the Fermi vectorpresented in Table I along with the values found for pure Cuand 1 ML of Ag on Cu by Bendounan et al.31 The bandwidthshift is not accompanied by a Fermi velocity renormalizationand is attributed to a simple charge transfer between thegraphene and the Cu(111).

As both the surface state and the graphene π band havean approximately circular Fermi surface the amount of chargetransfer can be related to the change in radius of the Fermisurface in both cases. Such analysis shows that the amountof charge transfer to the surface state is appreciably less thanto the graphene π bands. It is, therefore, expected that themajority of the charge transferred to the graphene layer comesfrom the bulk Cu and not the surface layer.

The presence of a surface superstructure has been shown toalter the effective mass31,32 as well as open a gap in the surfacestate at the surface brillouin zone boundary [∼0.151 A−1 for1 ML of Ag on Cu(111)].31 The absence of such a gap in thespectral function (Fig. 7) and the similarity of the effectivemass from clean Cu(111), ∼0.41, and graphene on Cu(111),∼0.39, indicates that no surface superstructure exists in thissystem. This is in agreement with the LEEM data, which in-dicated an oxygen superstructure on the graphene on Cu(100)sample but not on the graphene on Cu(111) sample. It is, there-fore, likely the presence of ordered, intercalated oxygen thatleads to the second doping level in the graphene on Cu(100)samples, which is not observed for graphene on Cu(111).

IV. CONCLUSION

We investigated graphene grown on single-crystal Cu(111)and Cu(100) surfaces. The graphene layers show a high degreeof rotational disorder, resulting in graphene K points forminga nearly unbroken arc in the diffraction space measurementsof both ARPES and LEED measurements. This rotationaldisorder was also observed in STM measurements.21 Thegraphene lattice does preferentially align with the Cu(111)lattice, though. The doping level, measured by the offset of theDirac crossing from the Fermi level (∼−0.3 eV), was foundto be similar for both substrates and to that found for grapheneon 1 ML of Cu/Ni(111) (∼−0.31 eV). On exposure to air,oxygen was found to intercalate under the graphene on theCu(100) surface, forming a superstructure and, consequently,a second doping level of the overlaying graphene. The dopinglevel of this second state is higher (∼−0.6 eV) due to morecharge transfer from the oxygen than the Cu. The size of thegap induced by interactions with the substrate was found tobe larger than for graphene on 1 ML of Cu/Ni(111) (250 and180 meV, respectively) and even larger for the intercalatedoxygen regions (∼350 meV). Interestingly, the interactionbetween graphene and the Cu(100) and Cu(111) surfacesappears to be similar due to identical doping levels and gaps,with a stronger interaction observed with the intercalatedoxygen. Similarly to previous studies,14 we find that the currentDFT theory underestimates the band gap (∼11 meV15) by afactor of 30. The Cu surface state at � on the Cu(111) surfaceis also found to be protected under the graphene, with only adoping derived binding energy shift being observed.

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ACKNOWLEDGMENTS

The Advanced Light Source is supported by the Director,Office of Science, Office of Basic Energy Sciences,of the US Department of Energy under Contract No.

DE-AC02-05CH11231. Work at Sandia was supported bythe Office of Basic Energy Sciences, Division of MaterialsSciences and Engineering of the US DOE under Contract No.DE-AC04-94AL85000. A.W. acknowledges support by theMax Planck Society.

*alwalter@lbl.gov1A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 (2007).2K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang,S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666(2004).

3W. Deheer, C. Berger, X. Wu, P. First, E. Conrad, X. Li, T. Li,M. Sprinkle, J. Hass, and M. Sadowski, Solid State Commun. 143,92 (2007).

4G. Rutter, J. Crain, N. Guisinger, and T. Li, Science 317, 219(2007).

5I. Forbeaux, J. M. Themlin, and J. M. Debever, Phys. Rev. B 58,16396 (1998).

6K. V. Emtsev, F. Speck, T. Seyller, L. Ley, and J. D. Riley, Phys.Rev. B 77, 155303 (2008).

7P. W. Sutter, J.-I. Flege, and E. A. Sutter, Nat. Mater. 7, 406 (2008).8Q. Yu, J. Lian, S. Siriponglert, H. Li, Y. P. Chen, and S.-S. Pei,Appl. Phys. Lett. 93, 113103 (2008).

9K. McCarty, P. Feibelman, E. Loginova, and N. Bartelt, Carbon 47,1806 (2009).

10E. Loginova, N. Bartelt, P. Feibelman, and K. F. McCarty, New J.Phys. 11, 063046 (2009).

11A. T. N’Diaye, S. Bleikamp, P. J. Feibelman, and T. Michely, Phys.Rev. Lett. 97, 215501 (2006).

12S. Bae et al., Nat. Nanotechnol. 5, 574 (2010).13J. M. Wofford, S. Nie, K. F. McCarty, N. C. Bartelt, and O. D.

Dubon, Nano Lett. 10, 4890 (2010).14A. Varykhalov, M. Scholz, T. Kim, and O. Rader, Phys. Rev. B 82,

121101(R) (2010).15G. Giovannetti, P. Khomyakov, G. Brocks, P. Kelly, and J. van den

Brink, Phys. Rev. B 76, 073103 (2007).16T. Ohta, F. El Gabaly, A. Bostwick, J. L. McChesney, K. V. Emtsev,

A. K. Schmid, Th. Seyller, K. Horn, and E. Rotenberg, New J. Phys.10, 023034 (2008).

17H. Hibino, S. Mizuno, H. Kageshima, M. Nagase, andH. Yamaguchi, Phys. Rev. B 80, 085406 (2009).

18R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Proper-ties of Carbon Nanotubes (Imperial College Press, London, 1998).

19A. Bostwick, T. Ohta, J. McChesney, T. Seyller, and E. Rotenberg,Solid State Commun. 143, 63 (2007).

20A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, Nat.Phys. 3, 36 (2006).

21H. I. Rasool, E. B. Song, M. Mecklenburg, B. C. Regan, K. L.Wang, B. H. Weiller, and J. K. Gimzewski, J. Am. Chem. Soc. 133,12536 (2011).

22Shu Nie, Joseph M. Wofford, Norman C. Bartell, Oscar D. Dubon,and Kevin F. McCarty, Phys. Rev. B 84, 155425 (2011).

23P. Gartland and B. Slagsvold, Phys. Rev. B 12, 4047 (1975).24S. D. Kevan, Phys. Rev. Lett. 50, 526 (1983).25P. A. Khomyakov, G. Giovannetti, P. C. Rusu, G. Brocks,

J. van den Brink, and P. J. Kelly, Phys. Rev. B 79, 195425(2009).

26I. Hamada and M. Otani, Phys. Rev. B 82, 153412 (2010).27The diffraction pattern in Fig. 3(c) has two sets of relatively sharp,

sixfold spots in contrast to the broad arcs in Fig. 3(b). This differenceresults from the smaller analysis area (2 vs. 20 μ). In the particularexample of Fig. 3(c), the two graphene orientations are rotated about37 and 45 from the labeled Cu spot (Ref. 13).

28R. Mayer, C.-S. Zhang, and K. G. Lynn, Phys. Rev. B 33, 8899(1986).

29F. Jensen, F. Besenbacher, E. Laegsgaard, and I. Stensgaard, Phys.Rev. B 42, 9206 (1990).

30W. Jacob, V. Dose, and A. Goldmann, Appl. Phys. A 41, 145 (1986).31A. Bendounan, F. Forster, J. Ziroff, F. Schmitt, and F. Reinert, Phys.

Rev. B 72, 075407 (2005).32F. Schiller, J. Cordon, D. Vyalikh, A. Rubio, and J. E. Ortega, Phys.

Rev. Lett. 94, 016103 (2005).

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